Non-purely transverse Magnus force in superconducting neutron stars

TL;DR

This paper investigates the forces on proton vortices in superconducting neutron star matter, revealing a significant longitudinal component of the Magnus force often neglected in previous studies.

Contribution

It provides a detailed analysis of momentum transfer and derives expressions for currents, highlighting a previously overlooked longitudinal Magnus force component.

Findings

Magnus force is the primary force on vortex cores in neutron star matter.

A correction to proton current near the vortex generates a longitudinal force component.

Results are relevant to other superconducting systems beyond neutron stars.

Abstract

The force acting on a proton vortex in extreme type-II superconducting neutron star matter is studied in the limit of vanishing temperature. A detailed analysis is presented on how momentum is transferred from length scales on the order of the London penetration depth to the vortex core. To examine the momentum flux, expressions for proton and electron currents are derived for arbitrary distances from the vortex line. It is shown that, in the regime of a large electron mean free path, the only force acting directly on the vortex core is the Magnus force. Notably, the correction to the proton current near the vortex core generates a component of the Magnus force aligned with the incident current measured far from the vortex. This contribution, responsible for longitudinal force, is usually overlooked in the literature. The results obtained in this work for a relatively simple problem concerning the force on a vortex in cold matter of neutron stars may also be relevant to other superconducting systems.